Devices and methods for decentralized voltage control

ABSTRACT

Devices and methods for the decentralized, coordinated control of the voltage of an electrical distribution system are provided. For example, a controller may include a network interface and data processing circuitry. The network interface may receive first measurements associated with a segment of an electrical distribution system and transmit a control signal configured to control equipment of the segment of the electrical distribution system. The data processing circuitry may run digital simulations of the segment of the electrical distribution system in various equipment configurations, selecting from among the various equipment configurations an equipment configuration that is expected to cause the voltage deviation of the segment to approach a desired value. The data processing circuitry then may generate the control signal, which may cause the equipment of the segment of the electrical distribution system to conform to the equipment configuration.

BACKGROUND

The subject matter disclosed herein relates to decentralized,coordinated control of equipment associated with an electricaldistribution system to optimize voltage to reduce power consumption.

Electrical power provided over an electrical distribution systemtypically must remain within a range of acceptable voltages (e.g., ±5%of 120V, or between approximately 114V and 126V). In an effort to keepthe voltages of the electrical distribution system within such a range,a variety of equipment may be placed throughout the distribution system.This equipment may include, for example, a load tap changing (LTC)transformer, voltage regulators, and distribution capacitor banks.Conventionally, each of these may be regulated according to adistributed control scheme, in which a local controller may individuallycontrol each piece of equipment. While a distributed control scheme maykeep the voltage of the electrical distribution system within theprescribed limits, it may not optimize other operational parameters,such as active power losses, power factor, and/or the flatness of thevoltage across a segment of the electrical distribution system.

BRIEF DESCRIPTION OF THE INVENTION

Certain embodiments commensurate in scope with the originally claimedinvention are summarized below. These embodiments are not intended tolimit the scope of the claimed invention, but rather these embodimentsare intended only to provide a brief summary of possible forms of theinvention. Indeed, the invention may encompass a variety of forms thatmay be similar to or different from the embodiments set forth below.

In a first embodiment, a controller may include a network interface anddata processing circuitry. The network interface may receive firstmeasurements associated with a segment of an electrical distributionsystem and transmit a control signal configured to control equipment ofthe segment of the electrical distribution system. The data processingcircuitry may run simulations of the segment of the electricaldistribution system in various equipment configurations, selecting fromamong the various equipment configurations an equipment configurationthat is expected to cause the voltage deviation of the segment toapproach a desired value (e.g., to be minimized). The data processingcircuitry then may generate the control signal, which may cause theequipment of the segment of the electrical distribution system toconform to the equipment configuration.

In a second embodiment, a method for controlling first and secondsegments of an electrical distribution system while the first segment isproviding power to a recovered portion of the second segment, usingrespective first and second application platforms, may include running avoltage control function on the second segment using the secondapplication platform, while the second application platform is runningthe voltage control function on the second segment, running a violationcheck function on the first segment using the first applicationplatform, and after running the voltage control function on the secondsegment using the second application platform, running the voltagecontrol function on the first segment using the first applicationplatform. The voltage control functions may cause a voltage deviation ofthe segments to respectively approach a desired value, and the violationcheck function may prevent or mitigate a voltage violation on the firstsegment.

In a third embodiment, an article of manufacture includes one or moretangible, machine-readable storage media having instructions encodedthereon for execution by a processor of an electronic device. Theseinstructions may include instructions to receive measurements associatedwith a feeder of an electrical distribution system and instructions tosimulate a distribution power flow on the feeder or use approximateequations according to various capacitor switching configurations of atleast one capacitor of the feeder using these measurements. In addition,the instructions may include instructions to determine an expectedvoltage deviation, reduction in power loss, and power factor on thefeeder associated with the various capacitor switching configurationsbased at least in part on the simulated distribution power flow on thefeeder or by using the approximate equations, instructions to select anon-dominated capacitor switching configuration from among the variouscapacitor switching configurations, and instructions to controlcapacitors of the feeder according to the non-dominated capacitorswitching configuration, thereby controlling the voltage deviation ofthe feeder.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentinvention will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIGS. 1 and 2 are one-line drawings of an electrical distribution systemthat can be optimized for voltage via decentralized coordinated control,in accordance with an embodiment;

FIG. 3 is a block diagram of a application platform of a substation thatcan optimize voltage of the electrical distribution system of FIGS. 1and/or 2 via decentralized coordinated control, in accordance with anembodiment;

FIGS. 4-8 represent equivalent circuits modeling segments of theelectrical distribution system of FIGS. 1 and/or 2, in accordance withan embodiment;

FIGS. 9-11 are schematic diagrams of measurement zones of a segment ofan electrical distribution system, in accordance with an embodiment;

FIG. 12 is a schematic diagram representing a manner of switchingdistribution capacitor banks to vary the operational parameters of asegment of an electrical distribution system, in accordance with anembodiment;

FIG. 13 is a flowchart describing an embodiment of a method fordecentralized coordinated control of an electrical distribution systemto optimize voltage, in accordance with an embodiment;

FIG. 14 is a plot modeling voltage over a segment of an electricaldistribution system before and after adjusting voltage regulators in themethod of the flowchart of FIG. 13, in accordance with an embodiment;

FIG. 15 is a one-line diagram illustrating a manner of supplying powerfrom a first segment of an electrical distribution system to a restoredsegment of the electrical distribution system, in accordance with anembodiment;

FIG. 16 is a one-line diagram representing an equivalent circuit of theone-line diagram of FIG. 15, in accordance with an embodiment;

FIG. 17 is a flowchart describing an embodiment of a method foroptimizing voltage across a first segment of an electrical distributionsystem and a restored segment of the electrical distribution system viadecentralized coordinated control;

FIG. 18 is a flowchart describing an embodiment of a method fordetermining a combination of capacitors of an electrical distributionsystem that may be switched on or off to optimize voltage;

FIG. 19 is a flowchart describing an embodiment of a method fordetermining a non-dominated capacitor combination solution thatoptimizes voltage;

FIG. 20 is a flowchart describing an embodiment of a method fordetermining a capacitor that may be switched on or off to optimizevoltage;

FIG. 21 is a flowchart describing an embodiment of a method fordetermining a non-dominated capacitor solution that optimizes voltage;

FIG. 22 is a plot representing a number of solutions that optimizevoltage in 3-D space;

FIG. 23 is a flowchart describing an embodiment of a method fordetermining and responding when switching is expected to cause a voltageviolation on the segment of the electrical distribution system;

FIG. 24 is a flowchart describing an embodiment of a method fordetecting and/or correcting any voltage violation that occurs when acapacitor is switched on or off;

FIG. 25 is a flowchart describing an embodiment of a method foradjusting voltage regulators across a segment of an electricaldistribution system after voltage has been optimized;

FIG. 26 is a flowchart describing an embodiment of a method for reducingthe voltage supplied by a substation to various segments of anelectrical distribution system after the voltage has been flattenedacross the segments;

FIG. 27 is a plot illustrating the reduction of the voltage across thesegments of the electrical distribution system, in accordance with anembodiment; and

FIG. 28 is a flowchart describing an embodiment of a method forperforming a distribution power flow simulation of a feeder of anelectrical distribution system.

DETAILED DESCRIPTION

One or more specific embodiments of the present invention will bedescribed below. In an effort to provide a concise description of theseembodiments, all features of an actual implementation may not bedescribed in the specification. It should be appreciated that in thedevelopment of any such actual implementation, as in any engineering ordesign project, numerous implementation-specific decisions must be madeto achieve the developers' specific goals, such as compliance withsystem-related and business-related constraints, which may vary from oneimplementation to another. Moreover, it should be appreciated that sucha development effort might be complex and time consuming, but wouldnevertheless be a routine undertaking of design, fabrication, andmanufacture for those of ordinary skill having the benefit of thisdisclosure.

When introducing elements of various embodiments of the presentinvention, the articles “a,” “an,” “the,” and “said” are intended tomean that there are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.

Embodiments of the present disclosure relate to techniques forcontrolling equipment on segments of an electrical distribution systemvia decentralized coordinated control. As used herein, the term“decentralized coordinated control” refers to a decentralized manner ofcontrolling electrical distribution system equipment (e.g., load tapchanging (LTC) transformers, voltage regulators, and/or distributioncapacitor banks) using an application platform for Volt/VAR optimizationlocated at the substation level and not in a utility back office. Thatis, rather than allowing each piece of equipment of the electricaldistribution system to operate independently according to a distributedcontrol scheme, the application platform for Volt/VAR optimization maycontrol many pieces of equipment in a segment of the electricaldistribution system in a coordinated manner. This decentralizedcoordinated control may be used to optimize various operationalparameters of the electrical distribution system, including, among otherthings, the voltage of the electrical distribution system. As usedherein, the term “optimize” means to generally improve overconventional, local control schemes. Thus, when a segment of anelectrical distribution system is optimized for voltage, the segment ofthe electrical distribution system may be understood to have a voltagebetter than would generally be obtained using conventional, localcontrol schemes. The terms “optimize” or “optimization” do not mean thatno other, better values of power factor are possible, only that thesevalues are improved or more closely approach a desired value thanconventional control schemes (e.g., a desired voltage deviation).

A segment of an electrical distribution system may include a feedersupplied with power by a substation. Accordingly, as will be discussedbelow, the application platform for Volt/VAR optimization may optimizecertain parameters (e.g., voltage or voltage deviation) at thesubstation level and/or the feeder level. In addition, using the samegeneral techniques, the application platform for Volt/VAR optimizationmay even optimize voltage on a segment of an electrical distributionsystem that has been restored after a fault.

FIGS. 1 and 2 represent two respective embodiments of segments of anelectrical distribution system 10 that can be optimized for voltageusing the decentralized coordinated control techniques described herein.In FIG. 1, a substation 12 feeds power directly to feeders 14 via a loadtap changing (LTC) transformer 16. In contrast, in FIG. 2, thesubstation 12 provides power to the feeders 14 via transformer withoutLTC and respective voltage regulators (VRs) 28. In either embodiment, aapplication platform 18, which may be associated with and/or located atthe substation 12, can optimize the electrical distribution system 10for voltage according to the decentralized coordinate control techniquesdiscussed herein. Moreover, although the following discussion refers toFIG. 1 in particular, any discussion of like elements of the embodimentof FIG. 1 should be understood as generally applicable to the embodimentof FIG. 2.

As noted above, FIG. 1 is a one-line diagram of the substation 12 thatmay supply power to the feeders 14 of the electrical distribution system10. The substation 12 may include, for example, a load tap changing(LTC) transformer 16 that transforms high side (HS) voltage to a lowside (LS) voltage within a defined range (e.g., so that the voltage onthe feeder is within 120V±5% (between 114V and 126V)). A applicationplatform 18 associated with the substation 12 may perform decentralizedcoordinated control of various equipment at the substation 12 or thefeeder 14, communicating with this equipment in any suitable way (e.g.,substation antenna 20). The application platform may optimize thevoltage of the substation 12 by controlling, alone or among otherthings, the operation of the LTC transformer 16 and/or distributioncapacitor banks 22. These distribution capacitor banks 22 are alsoreferred to herein as capacitors 22. When a capacitor 22 is on (e.g.,closed), some amount of reactive power (VAR) may be injected into thefeeder 14 through the capacitor 22. By varying which capacitors 22 areswitched on or off, the amount of reactive power may vary. Consequently,operational parameters of the electrical distribution system 10, such aspower factor, active power losses, voltage deviation over the length ofthe feeder 14, and so forth, may vary.

As shown in FIGS. 1 and 2, each feeder 14 supplies power to variousdistribution transformers 26 to loads 27. These loads 27 may drawvarying amounts of real power (W) and reactive power (VAR). Feeder powerfactor and voltage profile depend on the amount of active and reactivepower load on the feeder 14. To provide one brief example, power factor(i.e., the ratio of real power to total power drawn) on the feeders 14may be low in the summertime because many of the loads 27 may be highlyreactive induction motors for air conditioning. As the voltage across afeeder 14 drops or rises, LTC (or voltage regulators (VRs) 28alternately) may transform the voltage across the length of the feeder14 to keep the voltages within the defined range (e.g., between 114V and126V). The voltage regulators (VRs) 28 each may include a selectable tappositions that can be controlled from the application platform 18. Thesedifferent tap positions may cause a voltage regulator (VR) 28 toincrease or decrease the voltage on its low side (LS) bus to a differentdegree. Distributed generation (DG) 30 may inject power into the feeder14, effectively acting as an inverse load 27.

As mentioned above, to manage certain operational parameters of theelectrical distribution system 10 (e.g., the voltage on the electricaldistribution system 10), the application platform 18 may control thedistribution capacitor banks 22 and voltage regulators (VRs) 28 of thefeeders 14 and/or the LTC transformer 16 of the substation 12. Anapplication platform for Volt/VAR optimization 18, an example of whichappears in FIG. 3, may perform various algorithms to determine aconfiguration for the various equipment of the electrical distributionsystem 10 that may optimize the voltage. Although the applicationplatform for Volt/VAR optimization 18 is shown in FIG. 3 to be at thesubstation 12, the application platform for Volt/VAR optimization 18 mayinstead be at any other suitable location in the electrical distributionsystem 10. The application platform for Volt/VAR optimization mayinclude a processor 40, memory 42, and storage 44. Operably coupled tothe memory 42 and/or the storage 44, the processor 40 may carry out thepresently disclosed techniques based on instructions executable by theprocessor 42. These instructions may be stored using any suitablearticle of manufacture that includes one or more tangiblemachine-readable media at least collectively storing these instructions.The memory 42 and/or the nonvolatile storage 44 may represent sucharticles of manufacture capable of storing these instructions, and mayinclude, for example, random-access memory, read-only memory, rewritableflash memory, a hard drive, and/or optical discs.

A network interface 46 may receive a variety of measurements 48 from thefield devices directly or through the remote terminal units (RTUs) 20.Using these measurements, the application platform for Volt/VARoptimization 18 may simulate the feeders 14 in a variety of equipmentconfigurations (e.g., distribution capacitor bank 20 switchingconfigurations and/or LTC or voltage regulator (VR) 28 tap positions).Based at least partly on these simulations, the application platform forVolt/VAR optimization 18 may generate control signals 50 for controllingthe equipment substation 12 and/or feeders 14 to optimize the voltage.

The application platform for Volt/VAR optimization 18 may follow ageneral set of guidelines in carrying out the voltage optimizationtechniques disclosed herein. In particular, the control signals 50 fromthe application platform for Volt/VAR optimization 18 may control thecapacitors 22 and voltage regulators (VRs) 28 installed along the lengthof the feeder 14, and/or the capacitors 22 and the LTC transformer 16and/or voltage regulators (VRs) 28 installed at the substation 12. Toaid in simulation, geographical information for each feeder 14 may beknown by the application platform for Volt/VAR optimization 18, and allavailable measurements 48 from the equipment of the substation 12 andfeeders 14 may include some indication of the time the measurements 48were taken (e.g., the measurements 48 may be time-stamped). As will bediscussed below, these measurements 48 can be used by the applicationplatform for Volt/VAR optimization 18 to calculate unknown voltages andcurrent at nodes of the feeders 14. In addition, to aid certain otherapplication platforms for Volt/VAR optimization 18 that are controllingother feeders 14 of the electrical distribution system 10, theapplication platform for Volt/VAR optimization 18 may “publish” theminimum and maximum voltage and the equivalent impedance of each of thefeeders 14 under its control to these other application platforms forVolt/VAR optimization 18. Moreover, when the application platform forVolt/VAR optimization 18 is controlling a substation 12 and feeders 14,the application platform for Volt/VAR optimization 18 may not change thestatus or settings of the equipment of the substation 12 and the feeders14 at the same. Furthermore, the application platform for Volt/VARoptimization 18 may control the voltage regulators (VRs) 28 anddistribution capacitor banks 22 unless communication to the voltageregulators (VRs) 28 and distribution capacitor banks 22 fails. Whencommunication fails, the voltage regulators (VRs) 28 and distributioncapacitor banks 22 revert back to their local settings. Otherwise, thevoltage regulators (VRs) 28 and distribution capacitor banks 22 willremain under the control of the application platform for Volt/VARoptimization 18. Finally, when the application platform for Volt/VARoptimization 18 begins to carry out voltage optimization, the voltageregulator (VRs) 28 taps will initially be locked in their most recentposition.

It should be noted that application platform for Volt/Var optimization18 can control the capacitor banks 22 and/or voltage regulators (VRs) 28in a variety of ways. For example, the application platform for Volt/Varoptimization 18 may send settings to appropriate device controllers thatcan control the devices. Additionally or alternatively, the applicationplatform for Volt/Var optimization 18 may send commands to the capacitorbanks 22 and/or voltage regulators (VRs) 28 (e.g., TRIP/CLOSE for acapacitor bank 22 and RAISE/LOWER for the LTC transformer 16 or voltageregulator (VR) 28). It may be appreciated that sending commands to avoltage regulator (VR) 28 in the field may be slow at times, and thus itmay be more desirable to send changes in settings to the appropriatedevice controllers. In the present disclosure, both the direct issuingof commands to feeder 14 equipment and the changing of settings may bereferred to as providing or issuing a control signal or a command.

The application platform for Volt/VAR optimization 18 may follow theabove guidelines at least partly by relying on the measurements 48. Ageneral minimum set of measurements 48 may be given as follows: (1)voltage (magnitude) at the substation 12 low side (LS) bus, (2) voltage(magnitude) at capacitor 22 locations, (3) voltage (magnitude) at lowside (LS) locations of voltage regulators (VR) 28 and their tappositions, (4) kW and kVAr flows at capacitor 22 locations and alljunction points (e.g., points at which a lateral is connected to a mainfeeder 14) between capacitor 22 and voltage regulator (VR) 28 locationsand the substation 12, (5) kW and kVAr at the substation 12 low side(LS) bus and kW and kVAr measurements from each feeder 14(alternatively, kW and kVAr measurements from each feeder 14 andtransformer 16 test data may be used to calculate kW and kVAr a thesubstation 12 high side (HS) bus), (6) kW and kVAr demand from eachlarge commercial and/or industrial load 27 between the substation 12 andany of the capacitors 22, and (7) end of line (EOL) voltages (ifunavailable, the voltage drop between the last measurement point and theend of the feeder 14 may otherwise be provided in another manner). Inaddition, it should be noted that if the feeders 14 have any distributedgeneration (DG) 30, additional voltage measurement points may be neededbecause the minimum voltage of the feeder 14 may not be the end of line(EOL) voltage. Additionally or alternatively, the voltages on the feeder14 may be estimated using approximate equations. For such an approach,the impedance of the feeder 14 would need to be known or estimated

As mentioned above, the application platform for Volt/VAR optimization18 may optimize voltage based at least in part on a simulation of thedistribution power flow across the electrical distribution system 10.Equivalent circuit diagrams and one-line diagrams represented by FIGS.4-12, discussed below, generally illustrate the basis upon which theapplication platform for Volt/VAR optimization 18 may perform thissimulation of the distribution power flow across portions of theelectrical distribution system 10. Although the equivalent circuits ofFIGS. 4-12 represent approximations of actual segments of the electricaldistribution system 10, these approximations are believed to simulatesegments of the electrical distribution system 10 with sufficientaccuracy to enable the application platform for Volt/VAR optimization 18to optimize voltage profile in the electrical distribution system 10.

FIG. 4 presents a line-to-neutral equivalent circuit modeling a feeder14 with a line segment with impedance 52. In the equivalent circuit ofFIG. 4, this feeder 14 serves load 27, here represented as a singleequivalent load. Kirchhoff's Voltage Law applied to the circuit of FIG.4 gives the following:{tilde over (V)} _(S) ={tilde over (V)} _(R) +{tilde over (Z)}Ĩwhere {tilde over (Z)}=R+jX is the impedance 52 of the line segment. Thecurrent vector Ĩ appears in FIG. 4 alongside the equivalent circuit, andrepresents the sum of both real and reactive current componentsĨ=I_(R)+jI_(X). The voltage drop, V_(drop), across the line segment isdefined as a difference between the magnitudes of the source voltage{tilde over (V)}_(S) and the load voltage {tilde over (V)}_(R):ΔV _(drop) =|{tilde over (V)} _(S) |−|{tilde over (V)} _(R)|.

Because of the small phase angle difference between the source voltage{tilde over (V)}_(S) and the load voltage {tilde over (V)}_(R), asillustrated in a phasor diagram of FIG. 5, the voltage drop between thesource and load voltage is approximately equal to the real part of thevoltage drop across the impedance {tilde over (Z)}, or Δ{tilde over(V)}={tilde over (Z)}Ĩ:ΔV _(drop) ≈Re{{tilde over (Z)}Ĩ}=RI _(R) +XI _(X),where Ĩ=I_(R)+jI_(X).

The voltage drop ΔV_(drop) is a function of both R and X, where R ismostly a function of wire size and X is mostly a function of theconductor spacing. In the electrical distribution system 10, the ratioof ratio of X/R generally may be greater than 2. It therefore may benoted that the voltage drop ΔV_(drop) across a feeder 14 of theelectrical system 10 could be reduced by using larger, and usually moreexpensive, wires to lower the value of R, or by installing capacitors 22to reduce the flow on reactive power (VAR).

Indeed, as noted above, the electrical distribution system 10 mayinclude a variety of capacitors 22. Strategically switching thesecapacitors 22 on or off can effectively reduce the flow on reactivepower through the feeder 14. An equivalent circuit representing a feeder14 having a shunt capacitor 22 appears in FIG. 6. When the shuntcapacitor 22 is on, the shunt capacitor 22 will inject a current, I_(C),that reduces the imaginary component of the current, I_(X), and,accordingly, the magnitude of the total current I. The reduction of theimaginary component of the current I_(X) flowing through the linesegment will effectively reduce the amount of voltage drop ΔV_(drop)across the line segment. For the equivalent circuit shown in FIG. 6, thevoltage drop ΔV_(drop) may be given as:ΔV _(drop) ≈RI _(R) +X(I _(X) −I _(C)),and the voltage rise of the circuit of FIG. 6 may be given as:ΔV _(rise) ≈XI _(C).

It should be understood that the equation above may approximate theeffect of a capacitor 22 switching on the feeder 14 voltage profile.From this equation, it may be seen that if the capacitor 22 is thecapacitor is oversized (i.e., I_(X)−I_(C)<0), the system may beovercompensated and the voltage drop in the line segment ΔV_(drop) maybecome negative. Consequently, the load voltage, V_(R), may becomehigher than the source voltage, V_(S). This condition may occur ifcapacitors 22 installed on the feeder 14 were not adequately located orsized, or when certain sections of the feeder 14 need to beovercompensated to achieve better voltage flattening along the feeder 14and its laterals. The effect of switching the capacitor 22 on or off inthe circuit of FIG. 6 may also effect power losses. The active powerloss on the line segment of the circuit of FIG. 6 while the capacitor 22is switched off (e.g., the condition illustrated by FIG. 4), may dependon the impudence 52 of the line segment and the square of the current,I, flowing through it:P _(loss) =RI ² =R(I _(R) ² +I _(X) ²)

These active power losses can also be calculated as:

$P_{loss} = {{\frac{R}{V_{R}^{2}}\left( {P^{2} + Q^{2}} \right)\mspace{14mu}{or}\mspace{14mu} P_{loss}} = {{\Delta\; V^{2}\frac{R}{Z^{2}}} \approx {\Delta\; V_{drop}^{2}\frac{R}{Z^{2}}}}}$

Switching on the shunt capacitor 22 in the circuit of FIG. 6 may reducea power loss component of the line segment due to the reactive powerflow, Q, (and the imaginary component of the current, I_(X)),consequently reducing the total power loss, as represented by thefollowing relationship:

P_(loss)^(new) = R(I_(R)² + (I_(X) − I_(C))²), or${P_{loss}^{new} = {\frac{R}{V_{R}^{2}}\left( {P^{2} + \left( {Q - Q_{C}} \right)^{2}} \right)}},{or}$$P_{loss} \approx {\left( {{\Delta\; V_{drop}} - {\Delta\; V_{rise}}} \right)^{2}{\frac{R}{Z^{2}}.}}$

Changes in the real power loss P loss of the line segment due toreactive compensation in the circuit can be calculated as:ΔP _(loss) ≈RI _(X) ² −R(I _(X) −I _(C))².

Here, it may be noted that if the capacitor 22 is oversized (i.e.,I_(X)−I_(C)<0), the circuit of FIG. 6 may be overcompensated. Likewise,the losses in the circuit will increase if I_(C)>2I_(X). The equationbelow may be used to approximate the effect of a capacitor 22 switchingon the active losses of the feeder 14:

${{\Delta\; P_{LOSS}} = {\sum\limits_{i,j}\left( {{R_{i,j}I_{X_{i,j}}^{2}} - {R_{i,j}\left( {I_{X_{i,j}} - I_{C_{k}}} \right)}^{2}} \right)}},$where R_(i,j) is a resistance of the line segment between nodes i and j,I_(X) _(i,j) is the imaginary component of the current on the linesegment between nodes i and j, and I_(C) _(k) is the current ofcapacitor k.

The power factor of a feeder 14 may also be affected by a capacitor 22.Namely, since power factor depends on the shift between the voltage andcurrent phasors (e.g., as illustrated in FIG. 5), the power factor ofthe substation 12 or feeder 14 may vary when a capacitor 22 is switchedon or off. Indeed, as shown by the phasor representation of FIG. 5, whenvoltage and current fall farther apart in terms of phase angle θ, (i.e.,as power factor worsens), a larger percentage of the power flow isreactive (VAR) rather than real (W). Power factor may be representedaccording to the following relationship:

${pf} = {{\cos(\theta)} = {\frac{P}{\sqrt{P^{2} + Q^{2}}}.}}$

Typically, the power factor may be lagging (i.e., the current phasor maybe “behind” the voltage phasor). From the equation above, it is apparentthat power factor may be a fraction ranging from 0 to 1. For example, apower factor of 1 means that there is no reactive power flowing in thecircuit, while a power factor of 0.9 means that 10% of the power is lostdue to reactive effects. It should be noted that during summer, powerfactor on a feeder 14 may be relatively low because of the high reactiveload of air conditioning induction motors during peak loading time.Off-season, both real and reactive loads are typically far below theirsummer values, and VAR loads lessen more than active power, so powerfactor on a feeder 14 may improve considerably at these times.

Since, as noted above, capacitors 22 switched on may inject opposingreactive power (VARs) into the system, as generally shown in FIG. 6,switching on such a capacitor 22 may affect the power factor of a feeder14 and/or a substation 12. A new power factor PF new that occurs when acapacitor 22 is switched may be modeled according to the followingequation:

${{pf}^{new} = {\frac{P - {\Delta\; P_{LOSS}}}{\sqrt{\left( {P - {\Delta\; P_{LOSS}}} \right)^{2} + \left( {Q - {\Delta\; Q_{LOSS}} - Q_{C}} \right)^{2}}} \approx \frac{P}{\sqrt{P^{2} + \left( {Q - Q_{C}} \right)^{2}}}}},$where ΔP_(LOSS) is the total active power loss reduction on the feeder14. This total active power loss reduction may be calculated as follows:

${{\Delta\; P_{LOSS}} = {\sum\limits_{i,j}{\Delta\; P_{{loss}_{i,j}}}}},$where i,j refer to a line segment in the electrical distribution system10 between two nodes i and j.

Likewise, ΔQ_(LOSS) represents the total reactive power loss reductionon the feeder 14, and may be calculated according to the followingrelationship:

${{\Delta\; Q_{LOSS}} = {\sum\limits_{i,j}{\Delta\; Q_{{loss}_{i,j}}}}},$where i,j refer to a line segment between two nodes i and j in theelectrical distribution system 10.

This reactive power loss reduction, ΔQ_(loss), may be calculatedaccording to the following equation:ΔQ _(loss) _(i,j) =X _(i,j) I _(X) _(i,j) ² −X _(i,j)(I _(X) _(i,j) −I_(C) _(k) ),where X_(i,j) is a reactance of the line segment between nodes i and j,I_(X) _(i,j) is the imaginary component of the current on the linesegment between buses i and j and I_(C) _(k) is the current of capacitork.

A feeder 14 may seldom have only one load 27, as illustrated in FIGS.4-6. As such, when the application platform 18 simulates the feeder 14,the application platform 18 may undertake additional calculations. Whenthe loads 27 are uniformly distributed (e.g., same rating distributionload tap changing (LTC) transformers 16 spaced uniformly over a lengthof a lateral segment of the electrical distribution system 10), asschematically represented in FIG. 7, it may not be necessary to modeleach load 27 to determine the total voltage drop from source to end overa length L. Under such conditions, the total voltage drop along a feeder14 may be given as:

${{\Delta\; V_{drop}^{total}} = {{Re}\left\{ {\frac{1}{2}\overset{\sim}{Z}\;{{\overset{\sim}{I}}_{t}\left( {1 + \frac{1}{n}} \right)}} \right\}}},$where {tilde over (Z)}=R+jX represents the total per phase impedancefrom the source to the end of the line and Ĩ_(t) represents the totalcurrent into the feeder 14. If the number of nodes is assumed to go toinfinity, the total three-phase power losses may be given by thefollowing relationship:

$V_{drop}^{total} = {{Re}{\left\{ {\frac{1}{2}\overset{\sim}{Z}\;{\overset{\sim}{I}}_{t}} \right\}.}}$

Total three-phase power losses thus may be given as:

$P_{loss}^{total} = {3\;{{{RI}_{t}^{2}\left( {\frac{1}{3} + \frac{1}{2\; n} + \frac{1}{6\; n^{2}}} \right)}.}}$

Accordingly, if the number of nodes of the feeder 14 goes to infinity,the three-phase power losses may be calculated according to thefollowing relationship:P _(loss) ^(total) =RI _(t) ².

Distribution Power Flow Simulation

As will be discussed below, the application platform for Volt/VARoptimization 18 may perform a distribution power flow simulation tosimulate the effect on a feeder 14 of various equipment configurations.By comparing various distribution power flow simulations for variousequipment configurations, the application platform for Volt/VARoptimization 18 may determine which of these configurations optimizevoltage of the feeder 14 and/or the substation 12. The applicationplatform for Volt/VAR optimization 18 may calculate the distributionpower flow on a distribution feeder 14 using backward/forward sweepiterative methods or through approximation equations. For example, asshown by a line-to-neutral equivalent circuit of a feeder 14 shown inFIG. 8, given the voltage at the substation {tilde over (V)}_(S), and aknown load 27 model at each feeder 14 bus (e.g., involving constantcomplex power, constant impedance, constant current, or some combinationthereof), a distribution power flow calculation may determine voltagesat all other buses, {tilde over (V)}_(i), where i=1, . . . , n, as wellas currents in each line section. The distribution power flow simulationmay determine (1) power flow in each section of the feeder 14 (e.g., kW,kVAr, and pf), (2) power loss in each section and total power loss, (3),total feeder power input in kW and kVAr, and (4) load kW and kVAr basedon a specified model of the load 27.

The application platform for Volt/VAR optimization 18 may perform adistribution power flow analysis using a backward/forward sweepiterative method. In a backward sweep, Kirchoff's Current Law (KCL) andKirchoff's Voltage Law (KVL) may be used to calculate voltage for eachupstream bus of a line or transformer branch. After performing such abackward sweep, a voltage mismatch at the low side (LS) bus of thesubstation 12 may be calculated. If the voltage mismatch is greater thansome tolerance, a forward sweep may be performed. In the forward sweep,Kirchoff's Voltage Law (KVL) may be used to compute the voltage for eachdownstream bus of the feeder 14, by using the specified source voltage,V_(S), and the line currents determined in the previous backward sweep.This iterative process may continue until the error in the magnitude ofthe substation 12 voltage V_(S) is within the tolerance.

Determining the distribution power flow for a feeder 14 without lateralsmay occur as illustrated by a flowchart 600 of FIG. 28. The flowchart600 may begin when the application platform for Volt/VAR optimization 18sorts buses of the feeder 14 according to their distance to thesubstation 12 and initializes the end node voltage as {tilde over(V)}_(n) ^(B)={tilde over (V)}_(S), where {tilde over (V)}_(S) is thespecified voltage at the substation bus LS and the superscript “B”stands for “backward sweep” (block 602). The application platform forVolt/VAR optimization 18 may start from the end bus and perform abackward sweep using KCL and KVL to calculate voltage of each upstreambus and the line currents (block 604). The backward sweep may take placeas follows:

Calculate the load current at the end node, n, as:

${{\overset{\sim}{I}}_{n}^{B} = \left( \frac{S_{n}^{B}}{{\overset{\sim}{V}}_{n}^{B}} \right)^{*}},$where S_(n) ^(B)=P_(n) ^(B)+jQ_(n) ^(B) is complex power at node n.Apply KCL to calculate the current flowing from node n to n−1:Ĩ _(n-1,n) ^(B) =Ĩ _(n) ^(B).Compute the voltage at node n−1 as:{tilde over (V)} _(n-1) ^(B) ={tilde over (V)} _(n) ^(B) +{tilde over(Z)} _(n) Ĩ _(n-1,n) ^(B).Calculate the load current at the node, n−1 as:

${\overset{\sim}{I}}_{n - 1}^{B} = {\left( \frac{S_{n - 1}^{B}}{{\overset{\sim}{V}}_{n - 1}^{B}} \right)^{*}.}$Compute the current flowing from node n−2 to node n−1 as:Ĩ _(n-2,n-1) ^(B) =Ĩ _(n-1) ^(B) +Ĩ _(n-1,n) ^(B).Compute the voltage at node n−2:{tilde over (V)} _(n-2) ^(B) ={tilde over (V)} _(n-1) ^(B) +{tilde over(Z)} _(n-1) Ĩ _(n-2,n-1) ^(B).The procedure continues until the substation voltage is calculated.

${{\overset{\sim}{V}}_{S}^{B} = {{\overset{\sim}{V}}_{1}^{B} + {{\overset{\sim}{Z}}_{1}{\overset{\sim}{I}}_{t}^{B}}}},{{where}\text{:}}$${\overset{\sim}{I}}_{t}^{B} = {\sum\limits_{i = 1}^{n}{{\overset{\sim}{I}}_{i}^{B}.}}$The application platform for Volt/VAR optimization 18 then may detectwhether the difference between the specified and calculated voltages,{tilde over (V)}_(S) and {tilde over (V)}_(S) ^(B) at the substation isless than the convergence tolerance, e (decision block 606):∥{tilde over (V)} _(S) |−|{tilde over (V)} _(S) ^(B)∥<ε.

If the above relationship is true, the simulation may be understood tobe reasonably accurate and the application platform for Volt/VARoptimization 18 may end its distribution power flow simulation (block608). Otherwise, the application platform for Volt/VAR optimization 18may perform a forward sweep using the specified source voltage, {tildeover (V)}_(S), and the currents calculated in the backward sweep ofblock 604 (block 610). The forward sweep of block 610 may be carriedout, for example, as follows:

A new voltage at node 1 is computed:{tilde over (V)} ₁ ^(F) ={tilde over (V)} _(S) −{tilde over (Z)} ₁ Ĩ_(t) ^(B),where superscript “F” stands for “forward sweep.”The forward sweep may continue at each node i until new voltages at allend nodes have been computed:

${\overset{\sim}{V}}_{i}^{F} = {{\overset{\sim}{V}}_{i - 1}^{F} - {{{\overset{\sim}{Z}}_{i}\left( {{\overset{\sim}{I}}_{t}^{B} - {\sum\limits_{j = 1}^{i - 1}{\overset{\sim}{I}}_{j}^{B}}} \right)}.}}$

After completing the forward sweep of block 610, the backward sweep maybe repeated (block 604) using the new end voltages (i.e., {tilde over(V)}_(n) ^(B)={tilde over (V)}_(n) ^(F)) rather than the assumed voltage{tilde over (V)}_(S) as carried out in the first iteration of thebackward sweep. The forward and backward sweeps of blocks 604 and 610may be repeated as shown in the flowchart 600 until the calculatedvoltage at the source is within the tolerance ε of the specified sourcevoltage {tilde over (V)}_(S).

If the feeder 14 has laterals, the specified voltage at the substationbus, {tilde over (V)}_(S), may be used as the initial voltage at the endnodes. The number of end nodes is equal to the number of the laterals ofthe feeder 14. The application platform for Volt/VAR optimization 18 maystart at the furthest node, which may be on the main feeder 14 or on alateral, and continue with a backward sweep until a first “junction”node (i.e., a node where the lateral branches in two directions) hasbeen reached. At this point, the application platform for Volt/VARoptimization 18 may “jump” to the end node of the branches connected tothis junction node, and may use the backward sweep until it reaches thejunction node again. After the backward sweep has been performed on allbranches, the number of the calculated voltages for this junction pointmay be understood to be equal to the number of the branches connected tothe junction. The upstream bus voltage of the junction bus then may becalculated using the most recent calculated junction bus voltage and thecalculated branch current between the two nodes.

The manners of performing the distribution power flow simulationdescribed above may involve assuming that before the power flow analysisof a distribution system, the three-phase voltages at the substation 12and the complex power at all of the loads 27, or load models, are known.However, if metering points are present along the feeder 14, it maydesirable to force the computed values to match the metered input.

For example, the input complex power (kW and kVAr) to a feeder 14 may beknown from the measurements 48 arriving at the application platform forVolt/VAR optimization 18 at the substation 12. This metered data in themeasurements 48 may represent, for example, total three-phase power orpower for each individual phase. If the input complex power to thefeeder 14 computed using the iterative distribution power flow processdescribed above does not match the measurements 48, the ratio of themeasurements 48 to the computed input may be calculated, and loads 27multiplied by this ratio. A few iterations of this iterativedistribution power flow process may be used to determine a new computedinput to the feeder 14. This new computed input should be closer to themetered input indicated by the measurements 48.

In general, when the application platform for Volt/VAR optimization 18simulates the distribution power flow across various segments of theelectrical distribution system, the application platform for Volt/VARoptimization 18 may follow the following process. First, the applicationplatform for Volt/VAR optimization 18 may calculate a ratio of themetered input from the measurements 48 and the input computed in thedistribution power flow process discussed above. Second, the applicationplatform for Volt/VAR optimization 18 may carry out the iterativedistribution power flow process discussed above again, repeating untilthe computed input falls within a tolerance of the metered inputindicated by the measurements 48.

A similar process may be performed when the measurements 48 indicatemetered data for other points on the feeder 14. For example, as shown byFIGS. 9-11, a distribution feeder 14 may be divided into measurementzones 58 that are bounded by end point measurements 60. These end pointmeasurements 60 may provide, for example, accurate branch active andreactive power flow measurements, voltage magnitude, and/or phasormeasurements. It should be appreciated that the end point measurements60 may be treated as boundary constraints, and that the measurementzones 58 may contain additional measurements within. Voltage magnitudesand voltage phase angles may be treated as specified voltages atmeasurement buses on the feeder 14. Calculated loads 27 in eachmeasurement zone 58 may be adjusted separately to meet boundaryconstraints indicated by the end point measurements 60. Note that whenan end point measurement 60, providing kW and kVAr, is present on thefeeder 14, only calculated loads 27 downstream from the end pointmeasurement 60 may be modified. The distribution power flow simulationacross a feeder 14 may be used to compute voltage rise ΔV, active powerloss reduction ΔP_(LOSS), and a new power factor that may occur wheneach of the distribution capacitor banks 22 of the feeder 14 is switchedon or off.

The active power loss reduction ΔP_(LOSS) due to the switching on of acapacitor 22 may be approximated as the sum of the reductions in theactive power losses in each line segment on the path from that capacitor22 to the substation 12 bus (for the moment we will neglect the lossesin distribution transformer). For example, as shown in FIG. 12, when acapacitor C2 is switched on, the reduction and active power losses maybe represented by the following equation:

Δ P_(LOSS_(C₂)) = Δ P_(loss_(C₂))^(S, 1) + Δ P_(loss_(C₂))^(1, 2),where

Δ P_(loss_(C₂))^(i, j) ≈ R_(i, j)I_(X_(i, j))² − R_(i, j)(I_(X_(i, j)) − I_(C₂))²represents loss reduction in line segment between nodes i and j due tocapacitor C₂, the value R_(i,j) is resistance of the line segmentbetween nodes i and jj, and the value

$I_{X_{i,j}} = {{Im}\left( {\overset{\sim}{I}}_{i,j} \right)}$is the imaginary component of the current Ĩ_(i,j) flowing between nodesi and j.

The reduction in the active power losses ΔP_(LOSS) loss due to theaddition of other capacitors 22 of the feeder 14 may be calculated in asimilar way, as follows:

     Δ P_(LOSS_(C₄)) = Δ P_(loss_(C₄))^(S, 1) + Δ P_(loss_(C₄))^(1, 2) + Δ P_(loss_(C₄))^(2, 3) + Δ P_(loss_(C₄))^(3, 4)     Δ P_(LOSS_(C_(3, 1))) = Δ P_(loss_(C_(3, 1)))^(S, 1) + Δ P_(loss_(C_(3, 1)))^(1, 2) + Δ P_(loss_(C_(3, 1)))^(2, 3) + Δ P_(loss_(C_(3, 1)))^(3, 31)Δ P_(LOSS_(C_(5, 1))) = Δ P_(loss_(C_(5, 1)))^(S, 1) + Δ P_(loss_(C_(5, 1)))^(1, 2) + Δ P_(loss_(C_(5, 1)))^(2, 3) + Δ P_(loss_(C_(5, 1)))^(3, 4) + Δ P_(loss_(C_(5, 1)))^(4, 5) + Δ P_(loss_(C_(5, 1)))^(5, 15)

The power factor may also be impacted by switching on the capacitors 22of the feeder 14. For example, the effect of switching on the capacitorC2 of FIG. 12 on the power factor at the substation 12 low side (LS) busS may be given as follows:

${{pf}_{C_{2}} \approx \frac{P_{t} - {\Delta\; P_{{LOSS}_{C_{2}}}}}{\sqrt{\left( {P_{t} - {\Delta\; P_{{LOSS}_{C_{2}}}}} \right)^{2} + \left( {Q_{t} - {\Delta\; Q_{{LOSS}_{C_{2}}}} - Q_{C_{2}}} \right)^{2}}}},{where}$Δ Q_(LOSS_(C₂)) = Δ Q_(loss_(C₂))^(S, 1) + Δ Q_(loss_(C₂))^(1, 2).

Voltage Optimization Objective Function

As will be discussed below, the application platform for Volt/VARoptimization 18 may optimize the voltage across the feeders 14 first byflattening the voltage and then by reducing it. The application platformfor Volt/VAR optimization 18 may attempt to flatten the voltage profilealong the feeders 14 and enable the feeders 14 to use deeper voltagereduction modes by minimizing the voltage deviations ΔV according to thefollowing objective:

Min Δ V subject  to V_(min) ≤ V_(j) ≤ V_(max), j = 1, …  , Npf_(min) ≤ pf ≤ pf_(max)

In the equation above, ΔV is the difference between the maximum and theminimum voltage on the feeder 14, N is the total number of feeder 14voltage measurement points, V_(min) is the minimum allowable voltage onthe feeder 14 (e.g., 120V−5%, or 114V), V_(max) is the maximum allowablevoltage on the feeder 14 as defined in the voltage flattening (VF)function (e.g., 120V+5%, or 126V), pf is the power factor measured atthe head of the feeder 14, and pf_(min) and pf_(max) are its lower andupper permissible limits as desired. As will be described further below,the application platform for Volt/VAR optimization 18 may determinewhich capacitor 22 or combinations of capacitors 22 may satisfy theabove relationship. Once the application platform for Volt/VARoptimization 18 has caused the voltage deviation ΔV across the feeders14 to be reduced, the application platform for Volt/VAR optimization 18may cause the source voltage V_(S) at the outset of the feeders 14 to bereduced.

When a feeder 14 has a normal configuration (i.e., no anomalousconditions on the feeder 14 or restored feeder 14 segments feed from thenormally configured source feeder 14), the application platform forVolt/VAR optimization 18 may carry out the voltage optimization functionin the manner represented by a flowchart 130 of FIG. 13. The flowchart130 may begin as the application platform for Volt/VAR optimization 18starts the voltage optimization function (block 132). As such, theapplication platform for Volt/VAR optimization 18 may obtainmeasurements 48, which may include LTC transformer 16, voltage regulator(VR) 28, and capacitor 22 status and voltage information directly fromremote terminal units (RTUs), from a database 49 that contains suchdata, or from the field (block 134).

Having obtained the measurements 48, the application platform forVolt/VAR optimization 18 may carry out a capacitor control function thatoptimizes voltage (block 136). This capacitor control function will bediscussed in greater detail below with reference to FIGS. 18-21 below.Essentially, the capacitor control function of block 136 may return acombination of capacitors 22 or a single capacitor 22 that, whenswitched on or off, may optimize voltage of the feeder 14. As will bediscussed below, the capacitor control function may involve simulatingthe feeder 14 in various configurations to determine a configurationthat best matches the [parameter function] objective relationshippresented above.

If the capacitor control function block 136 outputs acapacitor-switching configuration that switches on or off at least onecapacitor 22 in the feeder 14 (decision block 138), the applicationplatform for Volt/VAR optimization 138 may simulate the effects of thesecapacitor-switching configurations via distribution power flowsimulations or by using the approximate equations. Thus, as will bediscussed below, selecting from the next capacitor 22 that is availablefor switching in the capacitor-switching configuration (block 140), theapplication platform for Volt/VAR optimization 18 may perform a firstvoltage regulator function (block 142). An example of such a firstvoltage regulator function 142 is discussed in greater detail below withreference to FIG. 22. Essentially, the first voltage regulator functionof block 142 involves simulating the effect on the feeder 14 ofswitching on or off the selected capacitor 22 to ensure that no voltageviolations are expected to result. If the first voltage regulatorfunction of block 142 indicates that the selected capacitor 22 isexpected to produce a voltage violation (decision block 144), it willcalculate tap point and the application platform for Volt/VARoptimization 18 may issue control signals 50 to the equipment of thefeeder 14 to enact the determined configurations.

In particular, the application platform for Volt/VAR optimization 18 mayfirst move taps of voltage regulators (VRs) 28 to new positions, as mayhave been calculated during the first voltage regulator function (block142), starting from the head of the feeder 14 (block 146). Theapplication platform for Volt/VAR optimization 18 may continue to movetaps of the voltage regulators (VRs) 28 in T_(dr) intervals, which maylast, for example, approximately 10 s to 15 s. Next, the applicationplatform for Volt/VAR optimization 18 may cause the selected capacitor22 to be switched on or off and may start a timer of duration T_(c)(block 148). The duration T_(c) represents a capacitor switching timedelay, during which time the selected capacitor 22 will not beconsidered available for switching. In some embodiments, T_(c) may lastat least 5 minutes. Additionally or alternatively, T_(c) may becomeprogressively longer as the number of times the capacitor 22 has beenswitched increases. For example, once the capacitor 22 has been switchedon or off five times in a particular 24-hour period, the time T_(c) maybe set such that the capacitor 22 can no longer be switched for someextended duration (e.g., 24 more hours).

To ensure that the simulations performed by the application platform forVolt/VAR optimization 18 accurately predicted the effect of switching onthe selected capacitor 22 on the voltage of the feeder 14, theapplication platform for Volt/VAR optimization 18 next may run aviolation check function (block 150). The violation check function mayinvolve monitoring the actual measurements 48 of the feeder 14 followingthe changes in configuration of the equipment on the feeder 14, andtaking corrective measures, if appropriate. An example of such aviolation check function as carried out at block 150 is described ingreater detail below with reference to FIG. 24. The violation checkfunction of block 150 may be carried out until a time delay Td1 haspassed, in which T_(c)>>T_(d1). After the time delay T_(d1), the voltageoptimization function may start again, with the application platform forVolt/VAR optimization 18 obtaining new measurements at block 174.

Returning to decision block 144, if the first voltage regulator function142 indicates that switching on the selected capacitor 22 would resultin a voltage violation that could not be remedied by adjusting voltageregulator (VR) 28 taps, the process flow may return to decision block138. If the capacitor-switching configuration includes other availablecapacitors 22, the application platform for Volt/VAR optimization 18 mayselect the next capacitor from the list of capacitors 22 (block 140) andcarry out the first voltage regulator function (block 142) again.

Returning to decision block 138, it should be appreciated that any timethe list of available capacitors 22 from a capacitor-switchingconfiguration of the capacitor control function of block 136 is empty,there are no capacitors 22 of the feeder 14 that can be switched on oroff to optimize voltage without causing a voltage violation (i.e. thecapacitor list is empty). Under such conditions, the voltage may beconsidered optimized and the application platform for Volt/VARoptimization 18 may carry out a second voltage regulator function 154.The second voltage regulator function of block 154 may be used toflatten the overall voltage across the length of the feeder 14. Anexample of such a second voltage regulator function as carried out atblock 154 is described in greater detail below with reference to FIG.25.

Having flattened the voltage after reducing the total voltage deviationover the length of the feeder 14, the application platform for Volt/VARoptimization 18 may determine a lowest supply voltage V_(s) that willkeep all the voltages along the feeder within the bounds of acceptablevalues (block 156). As such, the application platform for Volt/VARoptimization 18 may also issue control signals to cause the LTCtransformer 16 and/or a first voltage regulator (VR) to lower the supplyvoltage V_(s). Because the supply voltage V_(s) is lowered, the totalpower consumed by the loads of the feeder 14 will be reducedaccordingly. Thereafter, the application platform for Volt/VARoptimization 18 may thereafter continue to optimize voltage according tothe flowchart 130.

Before continuing further, the effect of carrying out the second voltageregulator function of block 154 of FIG. 13 is briefly described withreference to FIG. 14. Specifically, FIG. 14 illustrates a plot 160,which includes an ordinate 162 representing the voltage across thelength of a feeder 14, as depicted above the plot 160. The voltages aredelineated as falling within 120V±5%, or 126V (line 164) and 114V (line166). An abscissa 168 represents a length of the feeder 14. As shown inFIG. 14, the feeder 14 includes two voltage regulators (VRs) 28. A curve172 represents the voltage across the feeder 14 before the secondvoltage regulator function of block 154 of FIG. 13 is carried out, and acurve 174 illustrates the voltage across the length of the feeder 14afterward. Thus, the second voltage regulator function of block 154causes the voltage regulators (VRs) 28 to generally output the samesupply voltage V_(S) as provided at the outset of the feeder 14 on theirrespective high side (HS) buses.

The voltage optimization function of FIG. 13 may also be employed tooptimize voltage of a normally configured feeder and a restored segmentof a different feeder 14 that had been subject to a fault. For example,as shown in FIG. 15, a first feeder 14A having power supplied by a firstsubstation 12A may supply power to a restored segment 180 of a secondfeeder 14B that is usually supplied by a substation 12B. As seen in FIG.15, a breaker 24 adjoining the first feeder 14A and the restored segment180 of the second feeder 14B is illustrated as closed. Thus, it may beunderstood that the first feeder 14A is supplying power to the restoredsegment 180 of the second feeder 14B in FIG. 15. The breaker 24 andswitch 124 on the other side of the restored segment 180 of the secondfeeder 14B are depicted as being open. A first application platform forVolt/VAR optimization 18A may be associated with the first feeder 14A,and a second application platform for Volt/VAR optimization 18B may beassociated with the second feeder 14B.

FIG. 16 represents the circuit of FIG. 15 in equivalent form. Namely,from the perspective of the first feeder 14A, restored segment 180 ofthe second feeder 14B may be seen as a load 27. From the perspective ofthe restored segment 180 of the second feeder 14B, disconnect switch 24is a source point that is supplying power to the restored segment 180.

The equivalent circuit of FIG. 16 may form a basis upon which tosimulate operational parameters of the feeders 14A and/or 14B forpurposes of optimizing voltage. Indeed, a flowchart 190 of FIG. 17illustrates one manner in which voltage may be optimized on both thefirst feeder 14A and the restored segment 180 of the second feeder 14B.The flowchart 190 of FIG. 17 may include two processes 192 and 194 thatare respectively carried out by different application platform forVolt/VAR optimizations 18. That is, the process 192 may be carried outby the first application platform for Volt/VAR optimization 18A that isassociated with the first feeder 14A, and the process 194 may be carriedout by the second application platform for Volt/VAR optimization 18Bthat is associated with the second feeder 14B. The processes 192 and 194may respectively begin with blocks 196 and 198 as the two applicationplatforms for Volt/VAR optimization 18 carry out voltage optimization.

The first application platform for Volt/VAR optimization 18A associatedwith the first feeder 14A may carry out a process 200 while the secondapplication platform for Volt/VAR optimization 18B associated with thesecond feeder 14B carries out a process 202. Specifically, the secondapplication platform for Volt/VAR optimization 18B may obtainmeasurements 48 pertaining to the equipment of the feeder 14B, includingthe restored segment 180. The application platform for Volt/VARoptimization 18B may also set an indicator IN (block 206) (e.g., IN=0)to indicate that the voltage optimization function is being carried outon the feeder 14B (block 208). The voltage optimization function ofblock 208 may be substantially the same as discussed above withreference to flowchart 130 of FIG. 13. After the application platformfor Volt/VAR optimization 18B has completed the voltage optimizationfunction of block 208, the application platform for Volt/VARoptimization 18B may set the indicator IN to indicate that the voltageoptimization is complete (block 210), (e.g., IN=1). Meanwhile, theapplication platform for Volt/VAR optimization 18B may occasionallypublish data 212 and 214 to the application platform for Volt/VARoptimization 18A, representing a minimum voltage V_(min) across thesecond feeder 14B and the indicator IN.

While the second application platform for Volt/VAR optimization 18B iscarrying out the voltage optimization function in process 202, the firstapplication platform for Volt/VAR optimization 18A may obtainmeasurements associated with the first feeder 14A (block 216) and carryout a violation check function (block 218) to ensure that the voltageoptimization carried out by the second application platform for Volt/VARoptimization 18B does not cause any voltage violations on the firstfeeder 14A. The violation check function of block 218 may besubstantially the same as the violation check function of block 150 ofFIG. 13, which is discussed in greater detail below with reference toFIG. 24. If the indicator 214 indicates that the second applicationplatform for Volt/VAR optimization 18A has not completed the voltageoptimization function (decision block 220), the first applicationplatform for Volt/VAR optimization 18A may continue to receive newmeasurements 48 and run the violation check function 218. Otherwise,when the second application platform 18B has completed the voltageoptimization function on the second feeder 14B, the processes 192 and194 both may progress to respectively carry out processes 222 and 224.

Namely, the second application platform for Volt/VAR optimization 18Bmay continue to provide the minimum voltage of the second feeder 14B,shown as data 226 while the first application platform for Volt/VARoptimization 18A carries out the process 222. That is, the firstapplication platform for Volt/VAR optimization 18A may set an indicatorIN (e.g., IN=0) (block 228) before carrying out the voltage optimizationfunction on the first feeder 14A (block 230). When the voltageoptimization function of block 230 has completed, the first applicationplatform for Volt/VAR optimization 18A may change the indicator IN tonote that the voltage optimization function of block 230 has completed(e.g., IN=1) (block 232).

Meanwhile, in the process 224, the second application platform forVolt/VAR optimization 18B may receive the indicator IN as data 234published by the first application platform for Volt/VAR optimization18A. As long as the data 234 suggests that the first applicationplatform for Volt/VAR optimization 18A has not completed the voltageoptimization function (e.g., IN=0) (decision block 236), the secondapplication platform for Volt/VAR optimization 18B may continue to wait(block 238). When the data 234 indicates that the first applicationplatform for Volt/VAR optimization 18A has completed the voltageoptimization function (e.g., IN=1) (decision block 236), both the feeder14A and the restored segment of the feeder 14B may be understood to beoptimized for voltage. The flowchart 190 of FIG. 17 may repeat asdesired.

Capacitor Control Function

FIGS. 18 and 19 represent an example of a method for carrying out thecapacitor control function for voltage of block 136 of FIG. 13. Asmentioned above, carrying out the method of FIG. 18 may produce a listof capacitors 22 of a feeder 14 that, when switched on or off, areexpected to optimize voltage on the feeder 14. In particular, FIG. 18represents a flowchart 240 that may begin when the application platformfor Volt/VAR optimization 18 simulates the taps of the voltageregulators (VRs) 28 of the feeder 14 as being in a neutral position(block 242). Under such conditions, the application platform forVolt/VAR optimization 18 may run a distribution power flow simulation inthe manner discussed above with reference to FIG. 28 (block 244) or useapproximate equations. Using any of the approaches, the applicationplatform for Volt/VAR optimization 18 may determine an initial voltagedeviation ΔV₀, representing a baseline voltage deviation that may beused for comparison purposes later (block 246).

Next, the application platform for Volt/VAR optimization 18 mayiteratively test various capacitor-switching configurations, each ofwhich may include a particular combination of capacitors 22 of thefeeder 14 switched on and/or off. Thus, the application platform forVolt/VAR optimization 18 may set a loop variable i=1 (block 248) andsimulate the effect of each i^(th) of 2^(M) capacitor-switchingconfigurations of combinations of capacitors 22 (block 250). Insimulating the feeder 14 with each i^(th) capacitor-switchingconfiguration, the application platform for Volt/VAR optimization 18 maydetermine the voltage deviation ΔV across the feeder 14, a reduction inactive power losses ΔP_(LOSS), and the power factor pf of the feeder 14(block 252). The application platform for Volt/VAR optimization 18 mayincrement i (block 254) and, while i is not greater than the totalnumber of capacitor-switching configurations (i.e., 2^(M)) (decisionblock 256), the application platform for Volt/VAR optimization 18 maycontinue to simulate the effect of various capacitor-switchingconfigurations on the feeder 14. After the voltage deviation ΔV,reduction in power losses ΔP_(LOSS) and power factors have beencalculated for all of the capacitor-switching configurations, theapplication platform for Volt/VAR optimization 18 may determine anon-dominated solution that optimizes voltage (block 258).

The application platform for Volt/VAR optimization 18 may carry outblock 258 of FIG. 18 in a variety of manners depending on the parameterbeing optimized. For example, a flowchart 270 of FIG. 19 represents onemanner of carrying out block 258 of FIG. 18, which may be used todetermine a non-dominated capacitor-switching configuration thatoptimizes voltage. The flowchart 270 may begin when the applicationplatform for Volt/VAR optimization 18 eliminates non-acceptablesolutions with respect to power factor, voltage limits (if no voltageregulators (VRs) 28 are present in the feeder 14), and voltage deviationmargin (block 272). The application platform for Volt/VAR optimization18 next may begin determining the non-dominated solutions (block 274)that may optimize voltage on the feeder 14 (block 274). Afterward, theapplication platform for Volt/VAR optimization 18 may determine thecapacitor-switching configuration that has the smallest voltagedeviation ΔV (block 276).

If more than one non-dominated solution has the smallest voltagedeviation ΔV (decision block 278), the application platform for Volt/VARoptimization 18 next may determine the switching configuration capacitorwith the highest power loss reduction ΔP_(LOSS) (block 280). If thenumber of non-dominated solutions for capacitor-switching configurationwith the highest power loss reduction ΔP_(LOSS) is greater than one, theapplication platform for Volt/VAR optimization 18 may select thecapacitor-switching configuration with the best power factor (block284). Next, the application platform for Volt/VAR optimization 18 maydetermine a switching order of the capacitors 22 in thecapacitor-switching configuration that produces optimal operationalparameters in the feeder 14 (block 286).

A variation of the flowchart of FIG. 18 for determining a capacitorswitching configuration that optimizes voltage deviation appears as aflowchart 290 of FIG. 20. The flowchart 290 may take place insubstantially the same manner as FIG. 18, with certain exceptions. Ingeneral, blocks 292-308 of FIG. 20 may take place in the same manner asblocks 242-258 of FIG. 18, except that blocks 300 and 306 of FIG. 20 aredifferent from blocks 250 and 256 of FIG. 18. Specifically, in block 300of the example of FIG. 20, the effect of a change in a single capacitor22, rather than a combination of capacitors 22, may be determined Thus,as indicated by decision block 306 of FIG. 20, the number of tests maybe reduced to M iterations rather than 2^(M) iterations, where Mrepresents the number of capacitors 22 that can be switched in thefeeder 14.

Likewise, FIG. 21 provides a flowchart 320 that is similar to theflowchart 270 of FIG. 19 for determining a non-dominated solution thatoptimizes the voltage deviation of the feeder 14. That is, blocks322-336 of FIG. 21 generally correspond to blocks 272-286 of FIG. 19,with certain exceptions. For example, because the method of theflowchart 320 of FIG. 21 relates to determining a non-dominated solutioninvolving switching only one capacitor 22, the non-dominated solutionselected by the flowchart 320 may represent the switching of only onecapacitor 22. For the same reason, there is no need to determine aswitching order of capacitors 22.

A 3-D plot 260 shown in FIG. 22 represents various solutions for voltagedeviation ΔV, power loss P_(LOSS), and power factor for variouscapacitor-switching configuration combinations, as generally may bedetermined in blocks 252 of the flowchart 240 of FIGS. 18 and 302 of theflowchart 290 of FIG. 20. In the 3-D plot 260, a first axis 262represents power losses P_(LOSS), a second axis 264 represents voltagedeviation ΔV, and a third axis 266 represents power factor (PF). A 3-Dsolution space 268 represents a 3-D boundary, within which varioussolutions for capacitor-switching configurations may produce acceptableresults. It should be appreciated that, from such a range of acceptablesolutions as may be found within the 3-D solution space 268 anon-dominated solution may be determined that optimizes voltage whileoffering the greatest active power loss reduction and/or most desirablepower factor for the feeder 14.

As described above with reference to FIG. 13, the application platformfor Volt/VAR optimization 18 may carry out a first voltage regulatorfunction at block 142, a violation check function at block 150, and asecond voltage regulator function at block 154. These functions will nowbe described in greater detail below.

First Voltage Regulator Function

One example of the first voltage regulator function that may be carriedout at block 142 of FIG. 13 appears as a flowchart 350 in FIG. 23. Tocarry out the first voltage regulator function of block 142 of FIG. 13,the application platform for Volt/VAR optimization 18 may begin thefunction (block 352), and set an indicator IN to a default value (e.g.,IN=1) (block 354). The application platform for Volt/VAR optimization 18then may run a distribution power flow simulation of the feeder 14 thatsimulates when a particular capacitor 22 is switched on or off andsimulating the voltage regulators (VRs) 28 at their current taps (block356) or use approximate equations to estimate the new voltage profile.If a maximum voltage on the feeder 14 exceeds a desired value (e.g.,V_(max)>126V) (decision block 358), the voltage regulators (VRs) 28 maybe adjusted to cause the maximum voltage to be reduced, if possible. Inparticular, the application platform for Volt/VAR optimization 18 mayiteratively adjust the voltage regulators (VRs) 28, starting with thefirst voltage regulator (VR) 28 that has a maximum voltage violation,starting from the head of the feeder 14 (block 360). The applicationplatform for Volt/VAR optimization 18 may calculate a different tapposition for the first voltage regulator (VR) 28 such that the newvoltage of the first voltage regulator (VR) 28 is less than the maximumallowable voltage V_(max) (block 362).

If the tap position calculated at block 362 is not feasible because itfalls lower than the capabilities of the first voltage regulator (VR) 28(decision block 364), the application platform for Volt/VAR optimization18 may indicate (block 366) that the selected capacitor 22 cannot beswitched without a voltage violation (e.g., IN=0), and the first voltageregulator function may end (block 368). If instead the tap positioncalculated at block 362 is a feasible tap position for the voltageregulator (VR) 28 (decision block 364), the application platform forVolt/VAR optimization 18 may run the distribution power flow simulationonce more (block 370), continuing to search for voltage violations.

Returning to decision block 358, when no maximum voltage violation isdetermined to occur anywhere on the feeder 14 (decision block 358), theapplication platform for Volt/VAR optimization 18 may ascertain whetherany minimum voltage violations occur across the feeder 14 (decisionblock 372). If no minimum voltage violations are simulated to occur onthe feeder 14 (e.g., V_(min)≧114V), the first voltage regulator functionmay end (block 368) while the indicator IN is set to indicate that theselected capacitor 22 can be switched on without a voltage violation(e.g., IN=1).

If a minimum voltage on the feeder 14 falls beneath a desired value(e.g., V_(min)<114V) (decision block 372), the voltage regulators (VRs)28 may be adjusted to cause the minimum voltage to be increased, ifpossible. In particular, the application platform for Volt/VARoptimization 18 may iteratively adjust the voltage regulators (VRs) 28,starting with the first voltage regulator (VR) 28 that has a minimumvoltage violation, starting from the head of the feeder 14 (block 374).The application platform for Volt/VAR optimization 18 may calculate adifferent tap position for the first voltage regulator (VR) 28 such thatthe new voltage of the first voltage regulator (VR) 28 is greater thanthe minimum allowable voltage V_(min) (block 376).

If the tap position calculated at block 376 is not feasible because itis higher than the capabilities of the first voltage regulator (VR) 28(decision block 378), the application platform for Volt/VAR optimization18 may indicate (block 366) that the selected capacitor 22 cannot beswitched without a voltage violation (e.g., IN=0), and the first voltageregulator function may end (block 368). If instead the tap positioncalculated at block 362 is a feasible tap position for the voltageregulator (VR) 28 (decision block 378), the application platform forVolt/VAR optimization 18 may run the distribution power flow simulationonce more (block 380) or use approximation method for determining thevoltage profile, continuing to search for voltage violations.

Violation Check Function

A flowchart 390 of FIG. 24 represents an example of the violation checkfunction of block 150 in FIG. 13, which represents a component of thevoltage optimization function. Recalling that the violation checkfunction of FIG. 24 may take place after a capacitor 22 has beenswitched at block 148 of FIG. 13, the violation check function offlowchart 390 may verify that no voltage violations have occurred afterthe capacitor 22 has been switched or, if a voltage violation hasoccurred occur, the violation check function of flowchart 390 may takecorrective action to mitigate the violations. The flowchart 390 maybegin when the application platform for Volt/VAR optimization 18 startsto carry out the violation check function (block 392) and obtains a newset of measurements 48 of the feeder 14 (block 394). The new set ofmeasurements 48 obtained by the application platform for Volt/VARoptimization 18 at block 394 may be used by the application platform forVolt/VAR optimization 18 to search for any voltage regulators (VRs) 28that exhibit a maximum voltage or minimum voltage violation (block 396).If no voltage violation is found (decision block 398), the applicationplatform for Volt/VAR optimization 18 may end the violation checkfunction (block 400).

In the event that switching the capacitor 22 at block 148 of FIG. 13,the flowchart 390 of FIG. 24 that represents an example of the block 150of FIG. 13 may cause the application platform for Volt/VAR optimization18 to undertake corrective measures. If a maximum voltage violation hasoccurred (decision block 398), the application platform for Volt/VARoptimization 18 first may identify the voltage regulator (VR) 28 nearestto the substation 12 exhibiting a maximum voltage violation (block 402).The application platform for Volt/VAR optimization 18 may calculate anew, lower tap position associated with the voltage regulator (VR) 28(block 404). If the calculated tap position is feasible (i.e., thecalculated tap position is not lower than the minimum tap positionavailable at the voltage regulator (VR) 28) (decision block 406), theapplication platform for Volt/VAR optimization 18 may output a controlsignal 50 to cause the voltage regulator (VR) 28 to lower its tap tothat calculated at block 404 (block 408). The application platform forVolt/VAR optimization 18 then may continue to verify that no othervoltage violations exist on the feeder 14, beginning again by obtaininga new set of measurements 48 (block 394). On the other hand, if thecalculated tap position is not feasible (i.e., the calculated tapposition is lower than a minimum available tap position of the voltageregulator (VR) 28) (decision block 406), the application platform forVolt/VAR optimization 18 may output a controller signal 50 to turn offthe largest capacitor 22 of the feeder 14 and/or furthest capacitor 22from the substation 12 (block 410).

If a minimum voltage violation has occurred (decision block 398), theapplication platform for Volt/VAR optimization 18 first may identify thevoltage regulator (VR) 28 nearest to the substation 12 exhibiting aminimum voltage violation (block 412). The application platform forVolt/VAR optimization 18 may calculate a new, higher tap positionassociated with the voltage regulator (VR) 28 (block 414). If thecalculated tap position is feasible (i.e., the calculated tap positionis not higher than the maximum tap position available at the voltageregulator (VR) 28) (decision block 416), the application platform forVolt/VAR optimization 18 may output a control signal 50 to cause thevoltage regulator (VR) 28 to raise its tap to that calculated at block414 (block 418). The application platform for Volt/VAR optimization 18then may continue to verify that no other voltage violations exist onthe feeder 14, beginning again by obtaining a new set of measurements 48(block 394). On the other hand, if the calculated tap position is notfeasible (i.e., the calculated tap position is higher than a maximumavailable tap position of the voltage regulator (VR) 28) (decision block416), the application platform for Volt/VAR optimization 18 may output acontroller signal 50 to turn on the largest capacitor 22 of the feeder14 and/or furthest capacitor 22 from the substation 12 (block 420).

Second Voltage Regulator Function

A flowchart 430 of FIG. 25 represents an example of the second voltageregulator function carried out by the application platform for Volt/VARoptimization 18 at block 154 of FIG. 13. As discussed above, this secondvoltage regulator function may cause the voltage regulators (VRs) 28across the feeder 14 to maintain, to a great extent, a low-side (LS) busoutput that is equal to the source voltage V_(S). The flowchart 430 ofFIG. 25, which represents an example of this second voltage regulatorfunction, may begin when the application platform for Volt/VARoptimization 18 starts the second voltage regulator function (block 432)and considers each voltage regulator (VR) 28 of the feeder 14iteratively (block 434). In particular, the application platform forVolt/VAR optimization 18 may begin with a first voltage regulator (VR)28 (e.g., VR_(i)), where initially i=1.

The application platform for Volt/VAR optimization 18 next may obtainnew measurements 48 associated with the voltage regulator (VR) 28 beingconsidered (VR_(i)) (block 436). In particular, the application platformfor Volt/VAR optimization 18 may receive measurements 48 indicating thecurrent tap position of the voltage regulator (VR) 28 being considered(VR_(i)) as well as low-side (LS) and low-side (LS) bus voltages of thevoltage regulator (VR) 28 being considered (VR_(i)).

The application platform for Volt/VAR optimization 18 may calculate anew tap position for the voltage regulator (VR) 28, such that themaximum voltage of the voltage regulator (VR) 28 being considered(VR_(i)) approaches the source voltage (block 438). If the calculatedtap position exceeds a maximum tap position capability of the voltageregulator (VR) 28 being considered (VR_(i)) (decision block 440), theapplication platform for Volt/VAR optimization 18 may set the tapposition to the maximum tap position (block 442). Otherwise, theapplication platform for Volt/VAR optimization 18 may change the tapposition of the voltage regulator (VR) 28 being considered (VR_(i)) tothe tap position calculated at block 438 (block 444).

Having caused the voltage regulator (VR) 28 being examined (VR_(i)) toswitch tap positions (if necessary), the application platform forVolt/VAR optimization 18 may receive new measurements 48 to verify thatthe maximum voltage has not exceeded the source voltage, adjusting thetap position of the voltage regulator (VR) 28 being examined (VR_(i)) asneeded (block 446). After waiting some time delay period T_(R) (block448), the application platform for Volt/VAR optimization 18 maydetermine whether any further voltage regulators (VRs) 28 are presentdownstream of the most recently examined voltage regulator (VR) 28(VR_(i)) (decision block 450). If so, the application platform forVolt/VAR optimization 18 may increment the value i (block 452) andcalculate once more a new tap position for the downstream voltageregulator (VR) 28 (VR_(i)) now being examined in the manner describedabove. Otherwise (decision block 450), the application platform forVolt/VAR optimization 18 may end the second voltage regulator function(block 454). When the second voltage regulator function ends at block454, the maximum voltage of the voltage regulators (VRs) 28 of thefeeder 14 should be close to the source voltage V_(s) without exceedingit.

Voltage Reduction Function

As noted above, when the voltage optimization function of FIG. 13 isrun, the voltage across the feeder 14 may be reduced after it has beenflattened via the voltage reduction function of block 156 of FIG. 13. Aflowchart 470 of FIG. 26 represents one example of this voltagereduction function undertaken at block 156 of FIG. 13. The flowchart 470of FIG. 26 may begin as the application platform for Volt/VARoptimization 18 starts the voltage reduction function (block 472),waiting until the application platform for Volt/VAR optimization 18 hasperformed the voltage flattening function as to all feeders associatedwith the substation 12 (block 474). Once the voltage flattening functionapplied across the feeders 14 have completed, the application platformfor Volt/VAR optimization 18 may determine the maximum and minimumvoltages of all the feeders using measurements 48 (block 476). If any ofthe maximum voltages of the feeders 14 exceeds a maximum acceptablevoltage (decision block 478), the application platform for Volt/VARoptimization 18 may cause the LTC 16 to tap down (block 480), and maywait for the violation check function for all of the feeders 14 tocomplete (block 482). Otherwise, the application platform for Volt/VARoptimization 18 may determine whether the minimum voltage of any of thefeeders 14 falls beneath a minimum acceptable voltage V_(min) (decisionblock 484). If so, the application platform for Volt/VAR optimization 18may cause the LTC 16 to tap up (block 486), before waiting for theviolation check function for all of the feeders 14 to complete (block482). Note that any successive tap changes should not exceed apredefined number of taps (e.g., 8 taps which is equivalent to 5%voltage change).

If the lowest measured voltages on all of the feeders 14 are such thatthe minimum is greater than the minimum plus a voltage margin, for aperiod longer than some configurable time delay TD1 (decision block488), the application platform for Volt/VAR optimization 18 may causethe LTC transformer 16 to tap down (block 480), continuing to do sountil the minimum voltage present on the feeders 14 approaches theminimum acceptable voltage V_(min). Note that any successive tap changesshould not exceed a predefined number of taps (e.g., 8 taps which isequivalent to 5% voltage change).

The application platform for Volt/VAR optimization 18 may thereafterwait for the second voltage regulator function to be completed for allfeeders 14 (block 490). If the second voltage regulator function resultsin any voltage regulator (VR) 28 tap changes occurring (decision block492), the application platform for Volt/VAR optimization 18 may wait forthe violation check function for all of the feeders 14 to complete(block 482) before returning to block 476 of the flowchart 470.Otherwise, the voltage reduction function may end (block 494).

As shown by a plot 510 of FIG. 27, the voltage reduction function ofFIG. 26 may effectively reduce the source voltage V_(S) to the greatestextent possible. The plot 510 of FIG. 27 includes an ordinate 512representing voltage along the feeders 14A and 14B, shown above the plot510. These voltages extend between a maximum acceptable voltage V_(max)at numeral 514, represented as 126 volts, and a minimum voltage V_(min)represented at numeral 516 as 114 volts. An abscissa 518 represents thelength of the feeders 14. As shown in the plot 510, curves 520 and 522represent the voltage level across the first feeder 14A and secondfeeder 14B, respectively, before the voltage reduction function of FIG.26 is carried out. Curves 524 and 526, on the other hand, represent thevoltage levels across the length of the feeders 14A and 14B,respectively, after performing the voltage reduction function of FIG.26. As can be seen, the curve 524 is lower than the corresponding curve520, and the curve 526 is lower than the corresponding curve 522. At alltimes, however, the curves 524 and 526 remain above the minimumacceptable voltage at numeral 516.

Technical effects of the present disclosure include, among other things,improved voltage flattening and reduction on a segment of an electricaldistribution system. Thus, according to embodiments of the presentdisclosure, loads of an electrical distribution system may consume lesspower from the segment of the electrical distribution system. Inaddition, the voltage control of a restored segment of an electricaldistribution system can also be undertaken using the same controlfunctions used to control a normally configured segment.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal language of the claims.

The invention claimed is:
 1. A first controller configured to providedecentralized coordinated control over a first segment of an electricaldistribution system supplied by a first substation while a secondcontroller is providing decentralized coordinated control over a secondsegment of the electrical distribution system supplied by a secondsubstation, the first controller comprising: a network interfaceconfigured to receive first measurements associated with the firstsegment of the electrical distribution system and transmit a controlsignal configured to control equipment of the first segment of theelectrical distribution system, wherein the first controller isconfigured not to control equipment of the second segment of theelectrical distribution system supplied by the second substation that iscontrolled by the second controller; and data processing circuitryconfigured to run first simulation of the first segment of theelectrical distribution system simulating various equipmentconfigurations based at least in part on the first measurements, toselect from among the various equipment configurations an equipmentconfiguration that is expected to cause a voltage deviation of the firstsegment of the electrical distribution system to approach a desiredvalue, and generate the control signal, wherein the control signal isconfigured to cause the equipment of the first segment of the electricaldistribution system to conform to the equipment configuration but not tocontrol equipment of the second segment; wherein the network interfaceis configured to communicate with the second controller at least duringa time the first segment is providing power to a recovered portion ofthe second segment providing decentralized coordinated control, andwherein the data processing circuitry comprises structure to control theequipment of the first segment based at least partly on communicationwith the second controller at least during the time the first segment isproviding power to the recovered portion of the second segment.
 2. Thecontroller of claim 1, wherein the control signal is configured tocontrol the equipment of the first segment of the electricaldistribution system, wherein the equipment comprises at least onecapacitor, and wherein the data processing circuitry is configured torun simulation of the first segment of the electrical distributionsystem simulating various equipment configurations, wherein the variousequipment configurations comprise various capacitor switchingconfigurations, and wherein the data processing circuitry is configuredto select from among the various capacitor switching configurations acapacitor switching configuration that is expected to cause the voltagedeviation of the first segment of the electrical distribution system toapproach the desired value.
 3. The controller of claim 2, wherein thecapacitor switching configuration indicates that a single one of aplurality of capacitors of the first segment of the electricaldistribution system is to be switched on or off.
 4. The controller ofclaim 2, wherein the capacitor switching configuration indicates that acombination of a plurality of capacitors of the first segment of theelectrical distribution system are to be switched on or off.
 5. Thecontroller of claim 4, wherein the data processing circuitry isconfigured to determine a switching order of the combination of theplurality of capacitors.
 6. The controller of claim 1, wherein thenetwork interface is configured to obtain the first measurements from aplurality of remote terminal units, wherein the first measurementscomprise: a voltage magnitude at a low side bus of the first substationof the first segment of the electrical distribution system; a voltagemagnitude at capacitors of the first segment of the electricaldistribution system; a voltage magnitude at lowside of voltageregulators of the first segment of the electrical distribution system;tap positions of the first segment voltage regulators; real and reactivepower flows at the first segment capacitors and at all junction pointsbetween the first segment capacitors and the first segment voltageregulators and the first substation; real and reactive power flows at ahigh side bus of the substation or real and reactive power flows fromeach feeder of the first segment of the electrical distribution system,or both; real and reactive demand from each commercial or industrial, orcommercial and industrial, load between the first substation and any ofthe first segment capacitors; and end of line voltages of the firstsegment of the electrical distribution system or a voltage drop betweena last measurement point and an end of a feeder.
 7. The controller ofclaim 1, wherein the data processing circuitry is configured todetermine a plurality of operational parameters of the first segment ofthe electrical distribution that are expected to vary depending on thevarious equipment configurations, wherein the plurality of operationalparameters comprises the voltage deviation over the first segment of theelectrical distribution system and: a power factor of the first segmentof the electrical distribution system; or a reduction in power lossesover the first segment of the electrical distribution system; or both.8. The controller of claim 7, wherein the data processing circuitry isconfigured to determine, after determining the equipment configurationthat is expected to cause the voltage deviation of the first segment ofthe electrical distribution system to approach the desired value, areduced supply voltage that is lower than a normal supply voltage to thefirst segment of the electrical distribution system and that is notexpected to result in a voltage violation when the equipment of thefirst segment of the electrical distribution system conforms to theequipment configuration.
 9. The controller of claim 7, wherein the dataprocessing circuitry is configured to select the equipment configurationfrom among the various equipment configurations by: selecting one ormore first equipment configurations that are expected to cause thevoltage deviation to most closely approach the desired value from amongthe various equipment configurations; selecting one or more secondequipment configurations that are expected to cause active power lossesto be reduced the most from among the one or more first equipmentconfigurations; and selecting a final equipment configuration that isexpected to cause a power factor to most closely approach a desiredvalue from among the one or more second equipment configurations. 10.The controller of claim 1, wherein the data processing circuitry isconfigured to run second digital simulations of the first segment of theelectrical distribution system based at least in part on the selectedequipment configuration before generating the control signal todetermine whether the selected equipment configuration is expected tocause a voltage violation on the first segment of the electricaldistribution system and, when the selected equipment configuration isexpected to cause the voltage violation, to determine a tap position fora voltage regulator of the first segment of the electrical distributionsystem that is expected to prevent the voltage violation from occurring.11. The controller of claim 1, wherein the network interface isconfigured to receive second measurements associated with the firstsegment of the electrical distribution system a period of time aftertransmitting the control signal, wherein the second measurements reflectan actual effect of the equipment configuration on the first segment ofthe electrical distribution system, and wherein the data processingcircuitry is configured to determine whether the second measurementsindicate a voltage violation and, when the second measurements indicatethe voltage violation, to vary the equipment configuration to preventthe voltage violation.
 12. The controller of claim 11, wherein the dataprocessing circuitry is configured, when the second measurementsindicate the voltage violation, to identify a voltage regulator of thefirst segment of the electrical distribution system that is situatedclosest to the first substation of the electrical distribution system,to calculate a lower or higher tap position associated with the voltageregulator that is expected to prevent the voltage violation and, whenthe tap position is not higher than a maximum tap position or lower thana minimum tap position, to cause the voltage regulator to assume the tapposition and, when the tap position is higher than the maximum tapposition or lower than the minimum tap position, to cause a switchablecapacitor of the first segment of the electrical distribution systemthat is located furthest from the first substation of the electricaldistribution system or that is the largest capacitor of the firstsegment of the electrical distribution system to be switched on or off.13. The controller of claim 1, wherein the data processing circuitry isconfigured, after transmitting the control signal, to cause one or morevoltage regulators of the first segment of the electrical distributionsystem to cause a high side voltage of the one or more voltageregulators to be approximately equal to a low side voltage of asubstation that supplies voltage to the first segment of the electricaldistribution system.
 14. A method for controlling first and secondsegments of an electrical distribution system while the first segment isproviding power to a recovered portion of the second segment, usingrespective first and second application platforms, comprising: running avoltage control function on the second segment using the secondapplication platform, wherein the voltage control function is configuredto cause a voltage deviation over the second segment to approach adesired value; using the first segment to provide power to the recoveredportion; while the second application platform is running the voltagecontrol function on the second segment, running a violation checkfunction on the first segment using the first application platform,wherein the violation check function is configured to prevent ormitigate a voltage violation on the first segment; and after running thevoltage control function on the second segment using the secondapplication platform, running the voltage control function on the firstsegment using the first application platform, wherein the voltagecontrol function is configured to cause a voltage deviation of the firstsegment to approach the desired value.
 15. The method of claim 14,comprising communicating a minimum voltage of the second segment fromthe second application platform to the first application platform whilethe first application platform is running the violation check functionon the first segment or while the first application platform is runningthe voltage control function on the first segment, or both.
 16. Themethod of claim 14, comprising communicating from the second applicationplatform to the first application platform an indication that the secondapplication platform has finished running the voltage control functionwhen the second application platform has finished running the voltagecontrol function and communicating from the first application platformto the second application platform an indication that the firstapplication platform has finished running the voltage control functionwhen the first application platform has finished running the voltagecontrol function.
 17. The method of claim 14, comprising, while thefirst application platform is running the voltage control function onthe first segment, running a violation check function on the secondsegment using the second application platform, wherein the violationcheck function is configured to prevent or mitigate a voltage violationon the second segment.
 18. An article of manufacture comprising: one ormore tangible, non-transitory machine-readable storage media havinginstructions encoded thereon for execution by a processor of a firstelectronic device, the instructions configured to perform equipmentcontrol over a first feeder supplied by a first substation of anelectrical distribution system without controlling a second feedersupplied by a second substation of the electrical distribution systemthat is being controlled by a second electronic device, the instructionscomprising: instructions to receive measurements associated with thefirst feeder of the electrical distribution system; instructions tosimulate a distribution power flow of the first feeder according tovarious capacitor switching configurations of at least one capacitor ofthe first feeder using the measurements; instructions to determine anexpected voltage deviation, reduction in power loss, and power factorassociated with the various capacitor switching configurations based atleast in part on the simulated distribution power flow of the firstfeeder; instructions to select a non-dominated capacitor switchingconfiguration from among the various capacitor switching configurationsin which the voltage deviation most closely approaches a certain value;instructions to control capacitors of the first feeder according to thenon-dominated capacitor switching configuration but not to control anyequipment of the second feeder; and instructions to coordinate with thesecond electronic device by receiving information relating to the secondfeeder from the second electronic device at least during a time thefirst feeder is providing power to a recovered portion of the secondfeeder.
 19. The article of manufacture of claim 18, wherein theinstructions to simulate a distribution power flow of the first feedercomprise instructions to simulate an effect of distributed generation onthe first feeder.
 20. The article of manufacture of claim 18, comprisinginstructions to transmit at least one of the measurements to the secondelectronic device associated with the second feeder of the electricaldistribution system.